where I stress that this is a classical-classical information about
random variable \(\hat{s} \)  (pointer states on \(\mathcal {S}\) ) with measurement
outcomes on \(\mathcal {F}\) . If we want general \(\mathcal {S}\mathcal {E}\)  states, but still the
pure decoherence model, Eq. (REF ) and Eq. (REF ),
we have exactly the same form as Eq. (REF ) but the decoherence
factor (the pure state overlap) is replaced by the generalized measure
of overlap, \(\mathrm {tr}[\rho _{\left.k\right|1}^{1/2}\rho _{\left.k\right|2}^{1/2}]\) ,
see Ref. [1]} for these expressions
in terms of generic angles (between conditional states) and lengths
on the Bloch sphere for spins and Ref. [2]}
for photons.
